Concept

Gateaux derivative

Related lectures (31)

Weak Derivatives: Definition and Properties

Covers weak derivatives, their properties, and applications in functional analysis.

Functional Derivatives

Covers the concept of functional derivatives and their calculation process with examples.

Properties of Weak Derivatives

Explores weak derivatives in Sobolev spaces, discussing their properties and uniqueness.

Analyse II: Directional Derivative

Covers the concept and calculation of directional derivatives in multivariable calculus.

Tangent Planes and Implicit Functions

Explores tangent planes, implicit functions, and directional derivatives in relation to graphs of functions.

Optimal Control Theory: OCPs

Covers Optimal Control Theory, focusing on Optimal Control Problems (OCPs) and the calculus of variations.

Continuous Derivable Functions

Covers continuously derivable functions on open intervals with continuous derivatives and examples of different derivative orders.

Continuous Derivatives

Covers the concept of continuous derivatives and their application in analyzing functions and determining critical points.

Untitled

Complex Derivatives: Cauchy-Riemann Equations

Explores complex derivatives, Cauchy-Riemann equations, rules of derivation, and properties of holomorphic functions.

Descent methods and line search: Second Wolfe condition

Explores the second Wolfe condition, guiding step sizes based on the directional derivative increase.

Properties of Integrals

Covers properties of integrals and differentiation, focusing on exercise solutions and function behavior.

Adversarial Training: Mock Exam Solution

Discusses the solution to a mock exam problem on adversarial training and the uniqueness of solutions.

Analytic Infinite Derivative Gravity

Explores Analytic Infinite Derivative (AID) gravity, discussing infinite derivatives in gravity theories, UV completeness, and implications for quantum gravity.

Intermediate Value Theorem

Covers the Intermediate Value Theorem and its applications in finding solutions of equations and understanding the properties of continuous functions.

Derivability Conditions

Explores conditions for non-differentiability in multivariable calculus and the implications of the differentiability theorem.

Optimization Techniques

Covers optimization techniques and their application in solving real-world problems.

Differentiability and Tangent Planes

Explores differentiability in functions and tangent planes to surfaces.

Directional Derivative: Definitions and Examples

Covers the definition of directional derivatives and their applications in two dimensions.

Implicit Functions

Covers directional derivatives, implicit functions, and the concept of the maximum.